If log7(343) = x, what is the value of x?

If log7(343) = x, what is the value of x?

Correct Answer: 3

Step 1: Understand the equation log7(343) = x. This means we are looking for the power (x) to which 7 must be raised to get 343.
Step 2: Rewrite 343 as a power of 7. We know that 7 multiplied by itself 3 times equals 343, which can be written as 7^3.
Step 3: Now we can replace 343 in the original equation with 7^3. So, we have log7(7^3) = x.
Step 4: Use the property of logarithms that states logb(b^y) = y. Here, b is 7 and y is 3.
Step 5: Therefore, log7(7^3) simplifies to 3. So, x = 3.

Logarithms – Understanding the relationship between logarithms and exponents, specifically how to express a number as a power of its base.
Exponential Equations – Recognizing and manipulating exponential forms to solve logarithmic equations.